Questions About Stefan-Boltzmann Law

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Discussion Overview

The discussion revolves around the Stefan-Boltzmann law and its implications regarding the relationship between temperature and emitted energy from an object. Participants explore the effects of temperature changes on photon emission and energy, particularly in the context of practical examples like light bulbs.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the relationship between a 2 degrees Celsius increase in temperature and the resulting 16-fold increase in emitted energy, seeking clarification on whether this is due to an increase in the number of photons or the energy of individual photons.
  • Another participant suggests that the increase in emitted energy is "something in between," referencing Planck's law for further details.
  • There is a challenge regarding the accuracy of the 16-fold increase claim, with one participant expressing uncertainty about that specific number.
  • Participants discuss that while energy increases with temperature to the fourth power, this does not imply that a 2 K increase results in a 16-fold increase in power, which is only true if the temperature is doubled.
  • One participant reflects on their understanding of spectral radiance and its dependence on temperature, noting differences in energy at varying wavelengths.

Areas of Agreement / Disagreement

Participants express differing views on the implications of temperature changes on emitted energy, with some uncertainty about the specific numerical relationships involved. The discussion remains unresolved regarding the exact nature of the correlation between temperature, photon number, and energy.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about temperature changes and their effects on energy emission, as well as the dependence on definitions of terms like spectral radiance.

mp44
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Hi, I have a few questions about Stefan-Boltzmann's law. Let's say that the temerature of an object increases for 2 degrees Celsius, that means that the emmited energy of a surface of that object will increase 16 times. Is this happening because the number of photons is increased 16 times or is the energy of 1 photon increased 16 times or something in between? What is the correlation between temperature of an object and the number of photons it emmits (if one exists)? Let's say in the example of light bulb, if the temerature of a light bulb increases will the light bulb glow brighter, and if it does is it because of an increase of a number of photons or the increase of the energy of 1 photon?
 
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mp44 said:
Let's say that the temerature of an object increases for 2 degrees Celsius, that means that the emmited energy of a surface of that object will increase 16 times.
I forgot to say: are you sure about that number?
 
DrClaude said:
I forgot to say: are you sure about that number?
Pretty sure,the energy increases with temperature on the 4th,about Planck's law-my english is not that good
 
mp44 said:
Pretty sure,the energy increases with temperature on the 4th
But power ∝ T4 doesn't mean that if you increase by 2 K, power increases by a factor of 16. That is true if you double the temperature.

mp44 said:
about Planck's law-my english is not that good
The link I gave is to Wikipedia, where you may find a version in your language. And it's about the formulas, not the text. Just look at the figure at the top, which shows spectral radiance as a function of wavelength for different temperatures.
 
DrClaude said:
But power ∝ T4 doesn't mean that if you increase by 2 K, power increases by a factor of 16. That is true if you double the temperature.
Sorry,that is what I ment,my mistake.

The link I gave is to Wikipedia, where you may find a version in your language. And it's about the formulas, not the text. Just look at the figure at the top, which shows spectral radiance as a function of wavelength for different temperatures.
Sorry,that is what I ment,my mistake.
Version in my language isn't very helpful since it has only few lines,formulas don't help at all but the picture does.Let's if I got it right-spectral radiance is the density of the radiation,right? So for 5000 K spectral radiance (density) is about 12,5 for the 0,6 picometers wavelength and for 4000 K density is 4 but also there is a decrease in energy because the most freqent wavelength at that temperature is 1 picometers which has less energy than photon at 0,6.
 

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